The Boltzmann Equation for Uniform Shear Flow
Sign Up to like & getrecommendations! Published in 2021 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-021-01717-5
Abstract: The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in… read more here.
Keywords: boltzmann equation; shear flow; uniform shear;
Chapman–Enskog Analyses on the Gray Lattice Boltzmann Equation Method for Fluid Flow in Porous Media
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-018-2005-1
Abstract: The gray lattice Boltzmann equation (GLBE) method has recently been used to simulate fluid flow in porous media. It employs a partial bounce-back of populations (through a fractional coefficient θ, which represents the fraction of… read more here.
Keywords: gray lattice; flow porous; fluid flow; boltzmann equation ... See more keywords
On Derivation of the Poisson–Boltzmann Equation
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-020-02562-8
Abstract: Starting from the microscopic reduced Hartree–Fock equation, we derive the macroscopic linearized Poisson–Boltzmann equation for the electrostatic potential associated with the electron density. read more here.
Keywords: equation; derivation poisson; boltzmann equation; poisson boltzmann ... See more keywords
The Linear Boltzmann Equation in Column Experiments of Porous Media
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DOI: 10.1007/s11242-020-01393-1
Abstract: The use of the linear Boltzmann equation is proposed for transport in porous media in a column. By column experiments, we show that the breakthrough curve is reproduced by the linear Boltzmann equation. The advection–diffusion… read more here.
Keywords: column experiments; boltzmann equation; linear boltzmann; equation ... See more keywords
Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation
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DOI: 10.1016/j.aop.2017.08.032
Abstract: Abstract We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two… read more here.
Keywords: points flow; flow analysis; boltzmann equation; fixed points ... See more keywords
Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation
Sign Up to like & getrecommendations! Published in 2017 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2017.06.024
Abstract: This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence.… read more here.
Keywords: goal; moment; approximation; error ... See more keywords
Milne problem for the linear and linearized Boltzmann equations relevant to a binary gas mixture
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.12.003
Abstract: Abstract A stationary boundary-value problem for the Boltzmann equation in a half space is considered for a binary mixture of gases when the indata on the boundary are given for the both species. Under the… read more here.
Keywords: milne problem; problem linear; linearized boltzmann; boltzmann equation ... See more keywords
Space-time behavior of the solution to the Boltzmann equation with soft potentials
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2022.03.024
Abstract: Abstract. In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials (−2 < γ < 0) in the close to equilibrium setting, under some velocity decay assumption, but… read more here.
Keywords: time; time behavior; boltzmann equation; space time ... See more keywords
Global existence of solutions of the Boltzmann equation for Bose–Einstein particles with anisotropic initial data
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2018.09.010
Abstract: In this paper we prove the global in time existence and uniqueness of solutions of the spatially homogeneous Boltzmann equation for Bose-Einstein particles for the hard sphere model for bounded anisotropic initial data. The main… read more here.
Keywords: bose einstein; boltzmann equation; equation; einstein particles ... See more keywords
L2 solution of linear non-cutoff Boltzmann equation with boundary conditions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.04.073
Abstract: Abstract In this paper, we are concerned about the existence of solution to linear non-cutoff Boltzmann equation with boundary conditions. In [9] and [18] , the existence of the solutions to the kinetic equation and… read more here.
Keywords: linear non; cutoff boltzmann; boltzmann equation; equation ... See more keywords
Global existence and decay of solutions for soft potentials to the Fokker–Planck–Boltzmann equation without cut-off
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.123947
Abstract: Abstract This paper is concerned with the large-time behavior of classical solutions near a given global Maxwellian to the Cauchy problem of the Fokker–Planck–Boltzmann equation for non-cutoff soft potentials. Our analysis is based on the… read more here.
Keywords: global existence; fokker planck; soft potentials; boltzmann equation ... See more keywords